Methods and apparatus for diagnosis and/or prognosis of cancer

ABSTRACT

The subject invention concerns methods for the detection, diagnosis, and/or prognosis of cancer by analyzing centrosomal features. In one embodiment, a method includes receiving an image of one or more cells; selecting a region of interest in one cell; segmenting the region of interest to delineate at least one centrosomal; extracting one or more features from the segmented image; and analyzing the extracted features to diagnose cancer. In another embodiment, the progression of cancer can be predicted through analysis and classification of the extracted features. In one embodiment, the method can be performed by a quantitative cancer analysis system including a diagnosis module and/or a prognosis module. In one embodiment, the method can be performed using an image processing system.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is the National Stage of InternationalApplication Number PCT/US2010/001955, filed Jul. 13, 2010, which claimsthe benefit of U.S. Provisional Application Ser. No. 61/225,003, filedJul. 13, 2009, each of which is hereby incorporated by reference hereinin its entirety, including any figures, tables, or drawings.

FIELD OF INVENTION

This invention relates to the detection, diagnosis, and/or prognosis ofcancers. Specifically, the invention provides an imaging algorithm toanalyze centrosomal features in order to distinguish cancer cells fromnormal cells and prognose long term from short term survival cancerpatients.

BACKGROUND OF INVENTION

The centrosome is a cellular organelle that functions as the microtubuleorganizing center of interphase and mitotic cells (Nigg (2002)). Thecentrosome duplicates itself only once during each cell cycle withduplication beginning near the G1-S transition and completing during theG2 phase. Duplicated centrosomes separate to produce two mitotic spindlepoles that organize the mitotic apparatus. Centrosomes play criticalroles in processes that ensure proper segregation of chromosomes andmaintain the genetic stability of human cells (Shinmura et al. (2008);Fukasawa (2007)). Centrosomal defects were originally proposed to leadto aneuploidy and cancer in 1914 by Boveri (Wunderlich (2002); Brinkleyet al. (1998)). He saw that cancer cells commonly have centrosomaldefects including increased centrosome number and postulated thatchanges in centrosome functionality may be key to cancer formation.Centrosomal abnormalities are detected in various types of humancancers, e.g., cancers of the lung, breast, gall bladder, bone,pancreas, colorectal, head, neck, prostate and ovaries (Bourke et al.(2007); Saunders (2005)) and rarely observed in normal tissue (Saunders(2005)). It is believed that cancer cells commonly have centrosomaldefects. Most researches have found that centrosomal defects occurred ata very early premalignant stage of tumor formation, prior to theappearance of detectable lesions. Centrosomal defects have been found toincrease in severity during tumor progression. Recent evidence indicatesthat loss of centrosomal integrity may be a major cause of chromosomalinstability underlying various human cancers (Fukasawa (2007); Bourke etal. (2007); Lentini et al. (2007); Landen et al. (2007)). Aneuploidy ofnonsmall cell lung cancer is associated with centrosomal abnormalities(Jung et al. (2007)). In the lung, important findings suggest thatcentrosomal abnormalities may develop at a relatively early stage oflung carcinogenesis. Moreover, it was shown that stepwise progression ofcentrosome defects is associated with local lung tumor progression to amore advanced stage, and with accelerating the metastatic process oflung carcinoma cells (Koutsami et al. (2006)).

Lung cancer is the most common cause of cancer mortality for both menand women. In 2009, the American Cancer Society estimated the numbers oflung cancer cases were 219,440 and lung cancer resulted in 159,390deaths in the United States (Jemal et al. (2009)). In contrast,colorectal, breast, and prostate cancers combined were 117,890 deaths.Once diagnosed, prognosis and treatment depend upon lung cancer staging,which considers tumor size and extent, nodal involvement and distantmetastasis (AJCC, (1998)). The five-year survival rates by clinicalstages were IA 50%, IB 47%, IIA 36%, IIB 26%, IIIA 19%, IIIB 7%, and IV2% (Rami-Porta et al. (2009)). Cancer detected in early stages havehigher survival rate. Unfortunately, the prognosis of stage I lungcancer is highly variable. Post operative recurrence of stage Inon-small cell lung carcinoma (NSCLC) leads to early mortality inapproximately 40%, with current pathology indices unable to distinguishthose with poor prognosis (Woo, (2009)). In our preliminary data (35cases), there are four cases who have survived nine years or more (stillalive) and three deceased cases who survived four years or less (four,three, and two years, respectively) in stage IA; there are two caseswho've survived nine years or more (remain alive) and six deceased caseswho survived four years or less (one case survived less than one year,two cases survived one year, three cases survived four, three, twoyears, respectively) in stage IB. In our study of patients with stage Ilung cancer, clinical techniques could not distinguish stage I patientsinto long term survivors and short term survival (fatality) groups.Molecular prognostic and diagnostic cancer markers should have a highprevalence, and the techniques to measure these markers must have highsensitivity and specificity. Examination of tumor cell organelles ormarkers can provide a method to accurately diagnose and recognize theprognosis of individual stage I NSCLC to enable timely and personalizedadministration of therapy (Kwiatkowski et al. (1998); D'Amico et al.(2000); D'Amico (2002)).

BRIEF SUMMARY OF THE INVENTION

The subject invention concerns methods and apparatus for the detection,diagnosis, and/or prognosis of cancer in a person or animal by analyzingcentrosomal features. In one embodiment, a method of the inventionincludes receiving an image of one or more cells; selecting a region ofinterest in one cell; segmenting the region of interest in the one cellto delineate or isolate at least one centrosome; extracting one or morefeatures from the segmented image; and analyzing the extracted featuresto diagnose cancer. In another embodiment, the progression of cancer canbe predicted through analysis of the extracted features. In oneembodiment, methods of the invention can be performed by a quantitativecancer analysis system including a diagnosis module and/or a prognosismodule. In one embodiment, the method can be performed using an imageprocessing system. Methods of the invention can be used to distinguishlonger term cancer survival patients from shorter term cancer survivalpatients.

In one embodiment, a total of 11 centrosomal features are extracted,calculated, and analyzed using, for example, image processing andfeature analysis. The centrosomal features which can be utilized in themethods include counting centrosomal number per cell; calculatingcentrosomal size; checking centrosomal fragment; measuring centrosomalintensity and its standard deviation (2 features); and describingcentrosomal shape from different aspects (6 features). High resolutionimages of cells are acquired and then followed up with one or more ofimage pre-processing (e.g., image enhancement), segmentation, featureextraction, and statistical analysis. In one embodiment, the statisticalanalysis includes two-sample t-test and/or two-sample Kolmogorov-Smirnov(K-S) test. The features discussed herein are illustrative. Otherfeatures can be extracted and analyzed.

In the following detailed description of the preferred embodiments,reference is made to the accompanying drawings, which form a parthereof, and within which are shown by way of illustration specificembodiments by which the invention may be practiced. It is to beunderstood that other embodiments may be utilized and structural changesmay be made without departing from the scope of the invention.

BRIEF DESCRIPTION OF DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

FIGS. 1A-1H. FIGS. 1A and 1B are original images under 100×oil-immersion objective, for a total magnification of 1000×. FIGS. 1Cand 1D are two full color centrosome region of interest (ROI) imagestaken from FIGS. 1A and 1B, respectively. FIGS. 1E and 1F are histogramsof FIGS. 1C and 1D. FIGS. 1G and 1H are the red channel histograms ofFIGS. 1C and 1D. t in FIGS. 1G and 1H are optimized thresholds.

FIGS. 2A and 2B. FIG. 2A shows a color RGB image of region of interest(ROI) taken from untreated cancer cell image, which includes centrosomesbelonging to this cell. FIG. 2B shows an interpolated image of FIG. 2A,its size is twice that of the image in FIG. 2A. To balance the imageprocessing time and resolution of image, two times interpolation ischosen.

FIGS. 3A-3D. FIG. 3A: interpolated image. FIG. 3B: the red channel ofRGB FIG. 3A. This channel shows the signal from the 594 laser readingthe Alexa Fluor 594 secondary antibody bound to γ-Tubulin, allcentrosome information can be found in this channel. FIG. 3C: thesegmented image of FIG. 3B. This binary image will be used as the maskfor separating centrosomes from the background. FIG. 3D: centrosomes areisolated from other parts of the image. It is analyzed in the redchannel. It is ready for feature extraction.

FIGS. 4A-4E show comparisons of centrosomal features between normal anduntreated cancer cells. The box plots show the selected 5 features havedifferent medians and different distributions.

FIGS. 5A-5E show comparisons of Cumulative Distribution Functions (CDF)between normal and untreated cancer centrosomal features. The EmpiricalCDF plots show the selected 5 features have different distributions.

FIGS. 6A-6E. FIG. 6A is a tissue image, stained with γ-Tubulin antibody;in which centrosomes are shown as red spots. FIGS. 6B and 6C are twoRegions of Interest (ROI). Images selected from FIGS. 6A, 6D, and 6E aresegmentation images of FIGS. 6B and 6C, from which centrosomes areisolated from background and ready for feature extraction.

FIG. 7. The distribution of error rates reveals the variation of errorrates by feature number. The order of features is optimized by minimumredundancy—maximum relevance (MRMR) (Peng et al. (2005); Ding and Peng(2005)). It shows the error rate reaching the minimum when the featurenumber is six.

FIGS. 8A-8F show comparisons of mean and confidence interval for Stage INSCLC patients who survived 4 years (fatalities) and those who survived9 years (survivors). For all six features, there are obvious differencesbetween the means and there is no overlap for their confidenceintervals.

FIGS. 9A-9F show comparison of distribution (location and shape) for4-year (fatality) and 9-year (survivor) patients. For all six features,the six features have different distributions.

FIGS. 10A-10F show comparisons of median and distribution for 4-year(fatality) and 9-year (survivor) patients. For all six features, the sixfeatures have different medians and distributions.

FIG. 11 is a functional block diagram a quantitative cancer analysissystem in accordance with an embodiment of the subject invention.

FIG. 12 is a functional block diagram an image processing system inaccordance with an embodiment of the subject invention.

FIG. 13 is a flowchart of a method for diagnosing cancer in accordancewith an embodiment of the subject invention.

FIG. 14 is a flowchart of a method for prognosis of cancer in accordancewith an embodiment of the subject invention.

FIG. 15 shows the formulae used to obtain interpolation at point P inpre-processing.

DETAILED DESCRIPTION OF THE INVENTION

The subject invention concerns methods and apparatus for the detection,diagnosis, and/or prognosis of cancer in a person or animal by analyzingcentrosomal features. In one embodiment, the method includes receivingan image of one or more cells; selecting a region of interest in onecell; segmenting the region of interest in the one cell to delineate orisolate at least one centrosome; extracting one or more centrosomalfeatures from the segmented image; and analyzing the extracted featuresto detect, diagnose, or provide a prognosis of cancer. Optionally, theresults of the analysis can be subjected to a classifying process, e.g.,to classify whether a result falls into a cancer or normal category or along-term survivor or a short-term survivor category. In anotherembodiment, the progression of cancer can be predicted through analysisof the extracted features. In one embodiment, the method furthercomprises obtaining a sample of tissue or cells from the person oranimal. Cancer cells and tissues for analysis also may be obtained frombiopsy (including bronchial brushing or washing) or resected cancerspecimens, or from biological fluid samples (e.g., blood, saliva, lymph,etc.). Cancer cells may be formalin fixed and paraffin embedded orpreserved in OCT by flash freezing. Circulating tumor cells also may beobtained for analysis from samples of blood, sputum, or urine,immobilized on a slide or in the channels of a microfluidic device. Inone embodiment, the method can be performed by a quantitative canceranalysis system including a diagnosis module and/or a prognosis module.In one embodiment, the method can be performed using an image processingsystem. In one embodiment of the present invention, centrosomal featuresare quantitatively measured. Herein, several centrosomal features arediscussed, which can be extracted, calculated, and analyzed using imageprocessing, for example. In one embodiment, one centrosomal feature iscounting centrosomal number per cell, one feature is calculation ofcentrosomal size, one feature is checking centrosomal fragment, twofeatures are measures of centrosomal intensity and its standarddeviation, and six features are descriptions of centrosomal shape fromdifferent aspects. Other features that can be utilized in the subjectinvention include texture features, such as Angular second moment,Contrast, Correlation, Sum of squares: Variance, Inverse differencemoment, Sum average, Sum variance, Sum entropy, Entropy, Differencevariance, Difference entropy, Information measures of correlation, andMaximal correlation coefficient. Additional features that can be used inthe subject invention include consistency/heterogeneity of individualcentrosomal features (e.g., number, area, fragment, etc.). In oneembodiment, at least one, two, three, four, five, six, seven, eight,nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen,seventeen, eighteen, nineteen, twenty, twenty-one, twenty-two,twenty-three, twenty-four, or twenty-five centrosomal feature(s) is(are) extracted and analyzed. Centrosomal features that can be utilizedin the present invention include, but are not limited to, centrosomalnumber/cell, area, fragment, intensity, intensity standard deviation,area/box, aspect, mean diameter, perimeter ratio, roundness, fractaldimension, solidity, eccentricity, and some texture features. In aspecific embodiment, six centrosomal features are extracted andanalyzed. In an exemplified embodiment, the features extracted andanalyzed comprise number/cell, area, roundness, intensity, perimeterratio, and fractal dimension. In another specific embodiment, fivecentrosomal features are extracted and analyzed. In an exemplifiedembodiment, the features extracted and analyzed comprise centrosomenumber/cell, area, intensity, fragment, and aspect.

Results that support detection or diagnosis of cancer include, but arenot limited to, where centrosomal number/cell is increased compared tothe number/cell of normal cells; centrosomal area is deviated from thearea of normal cells; centrosomal intensity is deviated from theintensity of normal cells; there is centrosomal fragment compared to nofragment of normal cells; centrosomal aspect is deviated from the aspectof normal cells. In one embodiment, the results obtained with thepatient samples are compared to reference values of the extractedfeatures for normal cells. The results are preferably statisticallysignificant.

In one embodiment, high resolution images of tissue or cells can beacquired; then followed up with one or more of image pre-processing(e.g., image enhancement), image segmentation, feature extraction, andstatistical analysis. In an embodiment, the statistical analysisimplemented can be two-sample t-test and/or two-sampleKolmogorov-Smirnov test and/or Wilcoxon rank sum test. The featuresdiscussed herein are illustrative. Other features or combinations offeatures can be extracted and analyzed according to embodiments of thesubject invention.

In one embodiment of the invention, the results of the analysis of theextracted features are subject to classification. If cancer is diagnosedusing the subject method, then prognosis of the person or animal can bepredicted following classifying the results of feature analysis intovarious categories (e.g., survival vs. fatality). In a specificembodiment, results are classified into a long-term survival orshort-term survival category. In a specific embodiment, the extractedfeatures that are analyzed comprise centrosomal number/cell, area,roundness, intensity, perimeter ratio, and fractal dimension. In anexemplified embodiment, the results are classified based on majoritycriterion, wherein if a majority of the analyzed centrosomes of apatient are classified into a long-term survival category, the patientwill be given a prognosis for long-term survival, or if a majority ofthe analyzed centrosomes of a patient are classified into a short-termsurvival category, the patient will be given a prognosis for short-termsurvival. Results that support a prognosis of long-term survival ofcancer, in one embodiment, include where centrosomal number/cell isincreased compared to the number/cell from samples from short-termsurvivors; centrosomal area is decreased compared to the area fromsamples from short-term survivors; centrosomal roundness is decreasedcompared to the roundness from samples from short-term survivors;centrosomal intensity is increased compared to the intensity fromsamples from short-term survivors; centrosomal perimeter ratio isincreased compared to the perimeter ratio from samples from short-termsurvivors; centrosomal fractal dimension is decreased compared tofractal dimension from samples from short-term survivors. In oneembodiment, the results obtained with the patient samples are comparedto reference values of the extracted features for cells of long-termsurvivors and/or cells of short-term survivors. The results arepreferably statistically significant.

In an embodiment, cancer is detected or diagnosed in an early stage. Inanother embodiment, a method of the invention provides a prognosisconcerning treatment and/or survival of a cancer for a person or animal.Lung cancer is discussed herein as an illustrative example. Theinvention can be applied to other cancers including, for example,prostate cancer.

The subject invention can also be used to monitor and predict apatient's response to a cancer therapy (e.g., chemotherapy). Cells ortissue samples of a patients' cancer or tumor can be obtained andtreated with an anti cancer therapeutic agent and the centrosomes of thecells monitored for reversal of one or more defects observed incentrosomal amplification of cancerous cells. In one embodiment, cancercells can be analyzed using the methods of the subject invention todetermine if treatment with a particular therapeutic agent (e.g.,MLN8054, an Aurora kinase inhibitor, see Huck et al. (2010); Manfredi etal. (2007)) reverses or ameliorates mitotic spindle and segregationdefects and chromosomal instability that are typically observed incentrosome amplification of cancer and tumor cells. If the particulartreatment appears to have activity in reversing or amelioratingcentrosomal defects of the cancer or tumor cells, then the clinician canpredict that the tested treatment would be useful in treating thepatient and the patient can be administered the particular treatment ina manner deemed most clinically appropriate. Similarly, if a particulartreatment does not appear to have activity in reversing or amelioratingcentrosomal defects of the cancer or tumor cells, then the clinicianmight predict that the tested treatment would not be useful in treatingthe patient and may decide not to administer the particular treatment tothe patient and may determine that an alternate or modified treatmentwould be more likely to have a clinically beneficial effect for thepatient. The subject invention can also be used to assess the responseto a therapeutic treatment by evaluating centrosome amplification usingthe subject invention to assess the chromosomal instability associatedwith karyotypic convergence (Fukasawa (2008)). Changes in centrosomalfeatures can also be monitored during cancer or tumor treatment toassist in determining whether the particular treatment regimen orprotocol being administered to a patient is having a beneficial effecton destruction, reduction, or inhibition of the cancer or tumor. Forexample, if during treatment, there is minimal or no reversal oramelioration of defects associated with centrosomal amplification, thenthe patient's treatment might be modified or changed in a clinicallyappropriate manner.

FIG. 11 is a functional block diagram of a quantitative cancer analysissystem 1103 in accordance with an embodiment of the subject invention.The system 1103 is only an illustrative embodiment of the invention.Other embodiments of such a system may include more, fewer, or differentcomponents. Or the components shown may be differently arranged.

In the embodiment shown, the quantitative cancer analysis system 1103includes an input interface 1105, an output interface 1107, memory 1109for program storage and/or data storage, and a processor 1111 forprocessing information. In an embodiment, the input interface 1105includes an input device 1115 such as a mouse or other pointing device,a keyboard, or a communication device such a modem or other networkinterface. In a particular embodiment, the input device 1115 is animaging device such as a microscope. In another embodiment, thequantitative cancer analysis system 1103 is incorporated into an imageprocessing system such as the image processing system 1203 describedbelow. Other input devices for receiving information are known in theart and can be used with the subject invention. In an embodiment, theinput interface 1105 serves to translate data received from the inputdevice 1115 into a format usable by the quantitative cancer analysissystem 1103. Thus, the input device 1115 and the input interface 1105can be replaced without modifying the quantitative cancer analysissystem 1103 as known in the art. In an embodiment, the output interface1107 includes an output device 1117 such as a monitor, printer,projector, or other display device, a speaker or other audio device, ora communication device such as a modem. Other output devices forpresenting information are known in the art and can be used with thesubject invention. In an embodiment, the output interface 1107 serves totranslate data received from the quantitative cancer analysis system1103 into a format usable by the output device 1117. Thus, the outputdevice 1117 and the output interface 1107 can be replaced withoutmodifying the quantitative cancer analysis system 1103 as known in theart. In an embodiment, the quantitative cancer analysis system 1103includes an application interface 1119 for sharing information withother applications. For example, the quantitative cancer analysis system1103 can include an interface for communicating with an electronicmedical records system. In an embodiment, the memory 1109 includescomputer-readable media embodying a computer-program product asdescribed above. In an embodiment, the memory includes a database orother device for data storage. Other memory devices are known in the artand can be used with the subject invention. In an embodiment, thequantitative cancer analysis system 1103 includes multiple inputinterfaces 1105, output interfaces 1107, memories 1109, processors 1111,input devices 1115, output devices 1117, or APIs 1119.

In an embodiment, the quantitative cancer analysis system 1103 includesone or more program modules, such as a image processing module 1121, afeature selection/analysis module 1123, a classification module 1125, adiagnosis module 1127, and/or a prognosis module 1129, as furtherdescribed below.

FIG. 12 is a functional block diagram of an image processing system 1203in accordance with an embodiment of the subject invention. The system1203 is only an illustrative embodiment of the invention. Otherembodiments of such a system may include more, fewer, or differentcomponents. Or the components shown may be differently arranged.

In the embodiment shown, the image processing system 1203 includes oneor more of an input interface 1105, output interface 1107, memory 1109,processor 1111, input device 1115, output device 1117, and/orapplication interface 1119 as described above.

In an embodiment, the image sequence processing system 1203 includes oneor more program modules, such as a temporal alignment module 1221, alandmark identification module 1222, a training module 1223, aprediction module 1225, an interpolation module 1227, a refinementmodule 1229, and/or a classification module 1231, as further describedbelow.

FIG. 13 is a flowchart of a method 1301 for diagnosing cancer inaccordance with an embodiment of the subject invention. The method 1301is only an illustrative embodiment of the invention. Other embodimentsof such a method may include more, fewer, or different steps. Or thesteps shown may be differently arranged.

FIG. 14 is a flowchart of a method 1401 for prognosis of cancer inaccordance with an embodiment of the subject invention. The method 1401is only an illustrative embodiment of the invention. Other embodimentsof such a method may include more, fewer, or different steps. Or thesteps shown may be differently arranged.

In an embodiment, one or more of steps of a method for diagnosing cancerare performed by one or more suitably programmed computers. In aparticular embodiment, at least one of the method steps is performed bythe one or more suitably programmed computers. Computer-executableinstructions for performing these steps can be embodied on one or morecomputer-readable media as described below. In an embodiment, the one ormore suitably programmed computers incorporate a processing system asdescribed below. In an embodiment, the processing system is part of aquantitative cancer analysis system and/or image processing system.

In an embodiment, one or more of steps of a method for prognosis ofcancer are performed by one or more suitably programmed computers. In aparticular embodiment, at least one of the method steps is performed bythe one or more suitably programmed computers. Computer-executableinstructions for performing these steps can be embodied on one or morecomputer-readable media as described below. In an embodiment, the one ormore suitably programmed computers incorporate a processing system asdescribed below. In an embodiment, the processing system is part of aquantitative cancer analysis system and/or image processing system.

In an embodiment, computer-executable instructions for providing aninterface can be embodied on one or more computer-readable media asdescribed below. In an embodiment, the interface can be presented on oneor more suitably programmed computers. In an embodiment, the one or moresuitably programmed computers incorporate a processing system asdescribed below. In an embodiment, the processing system is part of aquantitative cancer analysis system and/or image processing system.

In an embodiment, one or more components of a data structure areembodied on one or more computer-readable media as described below. Inan embodiment, the data structure can be accessed via one or moresuitably programmed computers. In an embodiment, the one or moresuitably programmed computers incorporate a processing system asdescribed below. In an embodiment, the processing system is part of aquantitative cancer analysis system and/or image processing system.

Aspects of the invention can be described in the general context ofcomputer-executable instructions, such as program modules, beingexecuted by a computer. Generally, program modules include routines,programs, objects, components, data structures, etc., that performparticular tasks or implement particular abstract data types. Suchprogram modules can be implemented with hardware components, softwarecomponents, or a combination thereof. Moreover, those skilled in the artwill appreciate that the invention can be practiced with a variety ofcomputer-system configurations, including multiprocessor systems,microprocessor-based or programmable-consumer electronics,minicomputers, mainframe computers, and the like. Any number ofcomputer-systems and computer networks are acceptable for use with thepresent invention.

Specific hardware devices, programming languages, components, processes,protocols, formats, and numerous other details including operatingenvironments and the like are set forth to provide a thoroughunderstanding of the present invention. In other instances, structures,devices, and processes are shown in block-diagram form, rather than indetail, to avoid obscuring the present invention. But anordinary-skilled artisan would understand that the present invention canbe practiced without these specific details. Computer systems, servers,work stations, and other machines can be connected to one another acrossa communication medium including, for example, a network or networks.

As one skilled in the art will appreciate, embodiments of the presentinvention can be embodied as, among other things: a method, system, orcomputer-program product. Accordingly, the embodiments can take the formof a hardware embodiment, a software embodiment, or an embodimentcombining software and hardware. In an embodiment, the present inventiontakes the form of a computer-program product that includescomputer-useable instructions embodied on one or more computer-readablemedia. Methods, data structures, interfaces, and other aspects of theinvention described above can be embodied in such a computer-programproduct.

Computer-readable media include both volatile and nonvolatile media,removable and nonremovable media, and contemplate media readable by adatabase, a switch, and various other network devices. By way ofexample, and not limitation, computer-readable media incorporate mediaimplemented in any method or technology for storing information.Examples of stored information include computer-useable instructions,data structures, program modules, and other data representations. Mediaexamples include, but are not limited to, information-delivery media,RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM,digital versatile discs (DVD), holographic media or other optical discstorage, magnetic cassettes, magnetic tape, magnetic disk storage, andother magnetic storage devices. These technologies can store datamomentarily, temporarily, or permanently. In an embodiment,non-transitory media are used.

The invention can be practiced in distributed-computing environmentswhere tasks are performed by remote-processing devices that are linkedthrough a communications network or other communication medium. In adistributed-computing environment, program modules can be located inboth local and remote computer-storage media including memory storagedevices. The computer-useable instructions form an interface to allow acomputer to react according to a source of input. The instructionscooperate with other code segments or modules to initiate a variety oftasks in response to data received in conjunction with the source of thereceived data.

The present invention can be practiced in a network environment such asa communications network. Such networks are widely used to connectvarious types of network elements, such as routers, servers, gateways,and so forth. Further, the invention can be practiced in a multi-networkenvironment having various, connected public and/or private networks.

Communication between network elements can be wireless or wireline(wired). As will be appreciated by those skilled in the art,communication networks can take several different forms and can useseveral different communication protocols.

Embodiments of the subject invention can be embodied in a processingsystem. Components of the processing system can be housed on a singlecomputer or distributed across a network as is known in the art. In anembodiment, components of the processing system are distributed oncomputer-readable media. In an embodiment, a user can access theprocessing system via a client device. In an embodiment, some of thefunctions or the processing system can be stored and/or executed on sucha device. Such devices can take any of a variety of forms. By way ofexample, a client device may be a desktop, laptop, or tablet computer, apersonal digital assistant (PDA), an MP3 player, a communication devicesuch as a telephone, pager, email reader, or text messaging device, orany combination of these or other devices. In an embodiment, a clientdevice can connect to the processing system via a network. As discussedabove, the client device may communicate with the network using variousaccess technologies, both wireless and wireline. Moreover, the clientdevice may include one or more input and output interfaces that supportuser access to the processing system. Such user interfaces can furtherinclude various input and output devices which facilitate entry ofinformation by the user or presentation of information to the user. Suchinput and output devices can include, but are not limited to, a mouse,touch-pad, touch-screen, or other pointing device, a keyboard, a camera,a monitor, a microphone, a speaker, a printer, a scanner, among othersuch devices. As further discussed above, the client devices can supportvarious styles and types of client applications.

In one embodiment of a method of the invention, once detection,diagnosis, and/or prognosis is determined using the present invention,then treatment appropriate for the cancer diagnosed or prognosed in thepatient can be implemented. Treatment can include, for example, surgery,chemotherapy, radiotherapy, etc. An ordinarily skilled clinician candetermine an appropriate treatment regimen for a person or animal basedon the diagnosis or prognosis provided by the subject invention for theparticular cancer.

The methods of the present invention can be used with humans and otheranimals. The other animals contemplated within the scope of theinvention include domesticated, agricultural, or zoo- orcircus-maintained animals. Domesticated animals include, for example,dogs, cats, rabbits, ferrets, guinea pigs, hamsters, pigs, monkeys orother primates, and gerbils. Agricultural animals include, for example,horses, mules, donkeys, burros, cattle, cows, pigs, sheep, andalligators. Zoo- or circus-maintained animals include, for example,lions, tigers, bears, camels, giraffes, hippopotamuses, andrhinoceroses.

Examples of cancers that can be subject to diagnosis and/or prognosisusing methods of the present invention are listed in Table 12.

TABLE 12 Examples of Cancer Types Acute Lymphoblastic Leukemia, AdultHairy Cell Leukemia Acute Lymphoblastic Leukemia, Head and Neck CancerChildhood Hepatocellular (Liver) Cancer, Adult Acute Myeloid Leukemia,Adult (Primary) Acute Myeloid Leukemia, Childhood Hepatocellular (Liver)Cancer, Childhood Adrenocortical Carcinoma (Primary) AdrenocorticalCarcinoma, Childhood Hodgkin's Lymphoma, Adult AIDS-Related CancersHodgkin's Lymphoma, Childhood AIDS-Related Lymphoma Hodgkin's LymphomaDuring Pregnancy Anal Cancer Hypopharyngeal Cancer Astrocytoma,Childhood Cerebellar Hypothalamic and Visual Pathway Glioma,Astrocytoma, Childhood Cerebral Childhood Basal Cell CarcinomaIntraocular Melanoma Bile Duct Cancer, Extrahepatic Islet Cell Carcinoma(Endocrine Pancreas) Bladder Cancer Kaposi's Sarcoma Bladder Cancer,Childhood Kidney (Renal Cell) Cancer Bone Cancer, Osteosarcoma/MalignantKidney Cancer, Childhood Fibrous Histiocytoma Laryngeal Cancer BrainStem Glioma, Childhood Laryngeal Cancer, Childhood Brain Tumor, AdultLeukemia, Acute Lymphoblastic, Adult Brain Tumor, Brain Stem Glioma,Leukemia, Acute Lymphoblastic, Childhood Childhood Leukemia, AcuteMyeloid, Adult Brain Tumor, Cerebellar Astrocytoma, Leukemia, AcuteMyeloid, Childhood Childhood Leukemia, Chronic Lymphocytic Brain Tumor,Cerebral Leukemia, Chronic Myelogenous Astrocytoma/Malignant Glioma,Leukemia, Hairy Cell Childhood Lip and Oral Cavity Cancer Brain Tumor,Ependymoma, Childhood Liver Cancer, Adult (Primary) Brain Tumor,Medulloblastoma, Liver Cancer, Childhood (Primary) Childhood LungCancer, Non-Small Cell Brain Tumor, Supratentorial Primitive LungCancer, Small Cell Neuroectodermal Tumors, Childhood Lymphoma,AIDS-Related Brain Tumor, Visual Pathway and Lymphoma, Burkitt'sHypothalamic Glioma, Childhood Lymphoma, Cutaneous T-Cell, see MycosisBrain Tumor, Childhood Fungoides and Sézary Syndrome Breast CancerLymphoma, Hodgkin's, Adult Breast Cancer, Childhood Lymphoma, Hodgkin's,Childhood Breast Cancer, Male Lymphoma, Hodgkin's During PregnancyBronchial Adenomas/Carcinoids, Lymphoma, Non-Hodgkin's, Adult ChildhoodLymphoma, Non-Hodgkin's, Childhood Burkitt's Lymphoma Lymphoma,Non-Hodgkin's During Carcinoid Tumor, Childhood Pregnancy CarcinoidTumor, Gastrointestinal Lymphoma, Primary Central Nervous SystemCarcinoma of Unknown Primary Macroglobulinemia, Waldenström's CentralNervous System Lymphoma, Malignant Fibrous Histiocytoma of PrimaryBone/Osteosarcoma Cerebellar Astrocytoma, Childhood Medulloblastoma,Childhood Cerebral Astrocytoma/Malignant Melanoma Glioma, ChildhoodMelanoma, Intraocular (Eye) Cervical Cancer Merkel Cell CarcinomaChildhood Cancers Mesothelioma, Adult Malignant Chronic LymphocyticLeukemia Mesothelioma, Childhood Chronic Myelogenous Leukemia MetastaticSquamous Neck Cancer with Chronic Myeloproliferative Disorders OccultPrimary Colon Cancer Multiple Endocrine Neoplasia Syndrome, ColorectalCancer, Childhood Childhood Cutaneous T-Cell Lymphoma, see MultipleMyeloma/Plasma Cell Neoplasm Mycosis Fungoides and Sezary MycosisFungoides Syndrome Myelodysplastic Syndromes Endometrial CancerMyelodysplastic/Myeloproliferative Diseases Ependymoma, ChildhoodMyelogenous Leukemia, Chronic Esophageal Cancer Myeloid Leukemia, AdultAcute Esophageal Cancer, Childhood Myeloid Leukemia, Childhood AcuteEwing's Family of Tumors Myeloma, Multiple Extracranial Germ Cell Tumor,Myeloproliferative Disorders, Chronic Childhood Nasal Cavity andParanasal Sinus Cancer Extragonadal Germ Cell Tumor NasopharyngealCancer Extrahepatic Bile Duct Cancer Nasopharyngeal Cancer, ChildhoodEye Cancer, Intraocular Melanoma Neuroblastoma Eye Cancer,Retinoblastoma Non-Hodgkin's Lymphoma, Adult Gallbladder CancerNon-Hodgkin's Lymphoma, Childhood Gastric (Stomach) Cancer Non-Hodgkin'sLymphoma During Pregnancy Gastric (Stomach) Cancer, Childhood Non-SmallCell Lung Cancer Gastrointestinal Carcinoid Tumor Oral Cancer, ChildhoodGerm Cell Tumor, Extracranial, Oral Cavity Cancer, Lip and ChildhoodOropharyngeal Cancer Germ Cell Tumor, ExtragonadalOsteosarcoma/Malignant Fibrous Germ Cell Tumor, Ovarian Histiocytoma ofBone Gestational Trophoblastic Tumor Ovarian Cancer, Childhood Glioma,Adult Ovarian Epithelial Cancer Glioma, Childhood Brain Stem OvarianGerm Cell Tumor Glioma, Childhood Cerebral Ovarian Low MalignantPotential Tumor Astrocytoma Pancreatic Cancer Glioma, Childhood VisualPathway and Pancreatic Cancer, Childhood Hypothalamic Pancreatic Cancer,Islet Cell Skin Cancer (Melanoma) Paranasal Sinus and Nasal CavityCancer Skin Carcinoma, Merkel Cell Parathyroid Cancer Small Cell LungCancer Penile Cancer Small Intestine Cancer Pheochromocytoma Soft TissueSarcoma, Adult Pineoblastoma and Supratentorial Primitive Soft TissueSarcoma, Childhood Neuroectodermal Tumors, Childhood Squamous CellCarcinoma, see Skin Pituitary Tumor Cancer (non-Melanoma) Plasma CellNeoplasm/Multiple Myeloma Squamous Neck Cancer with OccultPleuropulmonary Blastoma Primary, Metastatic Pregnancy and Breast CancerStomach (Gastric) Cancer Pregnancy and Hodgkin's Lymphoma Stomach(Gastric) Cancer, Childhood Pregnancy and Non-Hodgkin's LymphomaSupratentorial Primitive Primary Central Nervous System LymphomaNeuroectodermal Tumors, Childhood Prostate Cancer T-Cell Lymphoma,Cutaneous, see Rectal Cancer Mycosis Fungoides and Sézary Renal Cell(Kidney) Cancer Syndrome Renal Cell (Kidney) Cancer, ChildhoodTesticular Cancer Renal Pelvis and Ureter, Transitional Cell Thymoma,Childhood Cancer Thymoma and Thymic Carcinoma Retinoblastoma ThyroidCancer Rhabdomyosarcoma, Childhood Thyroid Cancer, Childhood SalivaryGland Cancer Transitional Cell Cancer of the Renal Salivary GlandCancer, Childhood Pelvis and Ureter Sarcoma, Ewing's Family of TumorsTrophoblastic Tumor, Gestational Sarcoma, Kaposi's Unknown Primary Site,Carcinoma of, Sarcoma, Soft Tissue, Adult Adult Sarcoma, Soft Tissue,Childhood Unknown Primary Site, Cancer of, Sarcoma, Uterine ChildhoodSezary Syndrome Unusual Cancers of Childhood Skin Cancer (non-Melanoma)Ureter and Renal Pelvis, Transitional Skin Cancer, Childhood Cell CancerUrethral Cancer Uterine Cancer, Endometrial Uterine Sarcoma VaginalCancer Visual Pathway and Hypothalamic Glioma, Childhood Vulvar CancerWaldenström's Macroglobulinemia Wilms' Tumor

Example 1 Quantificational and Statistical Analysis of the Differencesin Centrosomal Features of Untreated Lung Cancer Cells and Normal Cells

Image Acquisition.

Images useable with the subject invention can be acquired using varioustechniques and equipment. In one embodiment, centrosomal images wereacquired in the Analytic Microscopy Core at the H. Lee Moffitt CancerCenter. A549 lung cancer cells and BEAS 2B normal bronchial epithelialcells were grown in RPMI with 10% FBS and BEGM supplemented with BEGMbullet kit, respectively. Cells were plated and grown on coverslips in a6-well plate at 37° C. with 5% CO₂. Cells were fixed using 4%Paraformaldehyde solution for 30 min at 4° C. and permeabilized using0.5% Triton X solution. Following blocking with 2% BSA, cells werestained with γ-Tubulin antibody (Sigma). Cells were then incubated withAlexaFluor 594 secondary antibody and mounted using ProLong Antifadewith DAPI (Invitrogen). A DMI6000 inverted Leica TCS AOBS SP5tandem-scanning confocal microscope was used to image the cells, under a100× oil immersion objective with scanning speed of 100-Hz per each2048×2048 frame, (FIGS. 1A and 1B). The LAS AF software suite was usedto image the cells and compile the max projections from Z-stacks. Theacquired image has a resolution of 75.7 nm. Other techniques andequipment can also be used.

Selection of Region of Interest (ROI).

In one embodiment, ROIs on an image are selected to include one cellwith at least one centrosome. In an exemplified embodiment, a total of606 untreated cancer ROIs and 57 normal ROIs were selected.

Pre-Processing.

Although some important centrosomal features of shape are preserved at75.7 nm resolution, in one embodiment, further resolution enhancement isused. Two dimensional first degree Lagrange interpolation polynomialscan also be implemented to enhance the resolution of images (Berrut andTrefethen (2004)). This is a linear interpolation technique which, atany point, uses information given only by the two adjacent pixels andleads to a good approximation of image boundaries. Linear interpolationis performed first in one direction, and then in the other. For example,in order to obtain interpolation at point P, one needs to interpolate atpoints R₁ and R₂ using information from Q₁₁, Q₂₁, and Q₁₂, Q₂₂,respectively. After that, interpolation at the point P is obtained usingthe formulae shown in FIG. 15.

This procedure provides the resolution enhancement which is necessaryfor successful feature extraction and measurement (see FIGS. 2A and 2B).

Other enhancement techniques can also be used with the present methods.For example, the contrast of the grayscale image I (red channel whichincludes centrosomal information) could be enhanced by transforming thevalues using contrast-limited adaptive histogram equalization (CLAHE)(Zuiderveld (1994)).

Image Segmentation.

Before extracting centrosomal features, the centrosomes can be isolatedfrom other parts of the cells in images (see FIGS. 3A-3D). Aftercomparing various thresholding methods, Kapur's maximum entropy-basedthresholding (Yin (2002)) was selected and implemented for this task dueto the consistency and accuracy of its outputs. The method considers theforeground (centrosomes) and the background (other parts of the cells)of an image as two different signal sources and finds the thresholdwhich maximizes the sum of the entropies of the two classes as follows.

Let an image have N pixels with gray level ranging from 0 to L−1. Denoteby h(i), the number of occurrences of gray level i, and by P_(i)=h(i)/N,the probability of occurrences of gray level i. The method findsthreshold t which maximizes

f(t) = H(0, t) + H(t, L) where${{H\left( {0,t} \right)} = {- {\sum\limits_{i = 0}^{t - 1}\;{\frac{P_{i}}{w_{0}}\ln\;\frac{P_{i}}{w_{0}}}}}},{w_{0} = {\sum\limits_{i = 0}^{t - 1}\; P_{i}}},{{H\left( {t,L} \right)} = {- {\sum\limits_{i = t}^{L - 1}\;{\frac{P_{i}}{w_{1}}\ln\;\frac{P_{i}}{w_{1}}}}}},{w_{1} = {\sum\limits_{i = t}^{L - 1}\;{P_{i}.}}}$

The entropy segmentation threshold depends upon the pixel number of thecentrosome space (P_(i)=h(i/N,), and dependents upon the number ofchannels. From FIGS. 1E and 1F, we can find different distributions ofpixel values (histograms) of these two color images. The entropythreshold didn't work well on these color images. We chose not to applythe entropy threshold on a full color image; instead, we applied theentropy threshold on only the red channel because having been stainedwith AlexaFluor 594, all centrosomal information can be found in thischannel. FIGS. 1G and 1H show the red channel histograms of the tworegion of interest (ROI) images. They have similar distributions withone peak. In fact, all the red channel histograms of centrosome ROIimages have similar monotonic distributions. After the optimizationprocedure, all the thresholds stopped on the right feet of the peaks. Wegot consistently accurate thresholds.

Features Extraction.

After centrosomes are separated, centrosomal features can be extracted,which can be later used for discrimination between cancer cells andnormal cells. Herein, 11 features are discussed that describe thecentrosome from different aspects, which include centrosomal number,size, shape, fragment, and intensity. The following is the definition ofthe 11 features.

1) Number: Centrosomal number per cell.

$N = {\sum\limits_{k = 1}^{\max\; k}\;\frac{k}{k}}$Centrosomal areas are marked as k=111 . . . , 333 . . . , 555 . . . , .. . in a labeled image.

2) Area: The number of pixels in the area of a centrosome.

$A = {\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{j = 0}^{n - 1}\;\frac{k\left( {i,j} \right)}{k}}}$k = 1, 3, 5  …Centrosomal areas are marked as k=111 . . . , 333 . . . , 555 . . . , .. . in a labeled image, k(i, j) is a pixel in the area and has samevalue with k. Other pixels are marked as 0. m, n are image sizes.

3) Fragment: Defective centrosomes may fragment into multiplemicrotubule organizing centers (Saunders (2005)).

$F = \left\{ \begin{matrix}1 & {{if}\mspace{14mu}{there}\mspace{14mu}{is}\mspace{14mu}{fragment}\mspace{14mu}{in}\mspace{14mu} a\mspace{14mu}{{centrosome}.}} \\0 & {{if}\mspace{14mu}{there}\mspace{14mu}{is}\mspace{14mu}{no}\mspace{14mu}{fragment}\mspace{14mu}{in}\mspace{14mu} a\mspace{14mu}{{centrosome}.}}\end{matrix} \right.$

4) Intensity: An average gray level intensity in a centrosomal area isobtained by adding pixel values over the centrosomal area and thendividing by the area of the centrosome.

$I = \frac{\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{j = 0}^{n - 1}\;{p_{k}\left( {i,j} \right)}}}{\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{j = 0}^{n - 1}\;\frac{k\left( {i,j} \right)}{k}}}$k = 1, 3, 5  …Centrosomal areas are marked as k=111 . . . , 333 . . . , 555 . . . , .. . in a labeled image, k(i, j) is a pixel in the area and has samevalue with k. Other pixels are marked as 0. p(i, j) is a gray value in acentrosomal area of a gray image.

5) Intensity standard deviation: The standard deviation of the graylevel intensity in the centrosomal area.

$\sigma = \sqrt{\frac{\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{j = 0}^{n - 1}\;\left\lbrack {{p_{k}\left( {i,j} \right)} - I} \right\rbrack^{2}}}{A - 1}}$A=area (in pixels), I=Intensity p(i, j) is a gray value in a centrosomalarea.

6) Area/Box: The ratio between the numbers of pixels in the area of acentrosome and the area of its bounding box. It is always less than orequal to 1.

${{Area}\text{/}{Box}} = \frac{\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{j = 0}^{n - 1}\;\frac{k\left( {i,j} \right)}{k}}}{{\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{j = 0}^{n - 1}\;\frac{k\left( {i,j} \right)}{k}}} + {\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{j = 0}^{n - 1}\;\frac{l\left( {i,j} \right)}{l}}}}$$\left\{ \begin{matrix}{{k = 1},3,{5\mspace{14mu}\ldots}} \\{{l = 2},4,{6\mspace{14mu}\ldots}}\end{matrix} \right.$Centrosomal areas are marked as k=111 . . . , 333 . . . , 555 . . . , .. . , in a labeled image, k(i, j) is a pixel in the area and has samevalue with k. Bounding box areas (not include centrosomal areas) aremarked as l=222 . . . , 444 . . . , 666 . . . , . . . in a labeledimage, l(i, j) is a pixel in the box and has same value with l.

7) Aspect: The ratio between the major axis and the minor axis of theellipse which is equivalent to a centrosome (has the same area as thecentrosome). Aspect is always greater than or equal to 1.

8) Mean Diameter: An average length of the diameters which are drawnthrough the centrosomal centroid at 2 degree increments.

To find the Mean diameter, we need to find the center of the area first.The Center of an area, which is denoted by Xc, Yc are given by the 1stmoment of the object.

${Xc} = \frac{\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{j = 0}^{n - 1}\;\frac{j \times {k\left( {i,j} \right)}}{k}}}{\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{j = 0}^{n - 1}\;\frac{k\left( {i,j} \right)}{k}}}$${Yc} = \frac{\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{j = 0}^{n - 1}\;\frac{i \times {k\left( {i,j} \right)}}{k}}}{\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{j = 0}^{n - 1}\;\frac{k\left( {i,j} \right)}{k}}}$k = 1, 3, 5  …${{Mean}\mspace{14mu}{diameter}} = \frac{\sum\limits_{\theta = 0}^{179}\;{d\left( {2\theta} \right)}}{180}$$\begin{matrix}{d -} & {{diameter},{{pass}\mspace{14mu}{through}}} \\\; & {{the}\mspace{14mu}{center}\mspace{14mu}{of}\mspace{14mu}{an}\mspace{14mu}{{area}.}} \\{\theta -} & {{rotation}\mspace{14mu}{angle}}\end{matrix}$

9) Perimeter ratio: The ratio between the convex perimeter of acentrosome and its actual perimeter. Perimeter ratio is always less thanor equal to 1.

${{Perimeter}\mspace{14mu}{ratio}} = \frac{\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{j = 0}^{n - 1}\;\frac{l_{1}\left( {i,j} \right)}{l_{1}}}}{\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{j = 0}^{n - 1}\;\frac{l_{2\;}\left( {i,j} \right)}{l_{2}}}}$$\left\{ \begin{matrix}{{l_{1} = 1},3,{5\mspace{14mu}\ldots}} \\{{l_{2} = 2},4,{6\mspace{14mu}\ldots}}\end{matrix} \right.$Convex perimeter pixels are marked as l₂=111 . . . , 333 . . . , 555 . .. , . . . , in a labeled image, l₁ (i, j) is a pixel on the convexperimeter and has same value with l₂. Perimeter pixels are marked asl₂=222 . . . , 444 . . . , 666 . . . , . . . , in a labeled image, l₂(i, j) is a pixel on the perimeter and has same value with l₂.

10) Roundness: Roundness is equal to the squared perimeter of acentrosome divided by 4πA, where A is the area of the centrosome.Roundness demonstrates how far the shape of the centrosome deviates froma circle. The larger the roundness parameter, the further the deviationof the shape from being round. If a centrosome has a circular shape, itsroundness is equal to one, otherwise, it is greater than one.

${Roundness} = \frac{\left\lbrack {\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{j = 0}^{n - 1}\;\frac{l\left( {i,j} \right)}{l}}} \right\rbrack^{2}}{4\pi{\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{j = 0}^{n - 1}\;\frac{k\left( {i,j} \right)}{k}}}}$$\left\{ \begin{matrix}{{k = 1},3,{5\mspace{14mu}\ldots}} \\{{l = 2},4,{6\mspace{14mu}{\ldots\mspace{14mu}.}}}\end{matrix} \right.$Centrosomal areas are marked as 111 . . . , 333 . . . , 555 . . . , . .. , in a labeled image, k(i, j) is a pixel in the area and has samevalue with k. Boundary areas are marked as 222 . . . , 444 . . . , 666 .. . , . . . in a labeled image, l(i, j) is a pixel in the boundary andhas same value with l.

11) Fractal dimension (Addison (1997)): The fractal dimension is ameasurement of roughness. The rougher the curve, the larger the fractaldimension. The general expression of fractal dimension is

${FD} = {\lim\limits_{S\rightarrow 0}\frac{\mathbb{d}\left( {\log(N)} \right)}{\mathbb{d}\left( {\log\left( {1\text{/}S} \right)} \right)}}$where N is the number of hypercubes (for example, square) of side lengthS required to cover the object (for example, a curve).

In practice, the box counting dimension can be estimated by selectingtwo sets of [log(N), log(1/S)] coordinates at small value of S. Anestimate of Fragment Dimension FD is then given by,

${FD} = {\frac{{\log\left( N_{2} \right)} - {\log\left( N_{1} \right)}}{{\log\left( {1\text{/}S_{2}} \right)} - {\log\left( {1\text{/}S_{1}} \right)}} = \frac{\log\frac{N_{2}}{N_{1}}}{\log\frac{S_{1}}{S_{2}}}}$

Other centrosomal features can be used and the features can beextracted, calculated, and/or measured differently. Additional featuresinclude, for example, measurement of Consistency/Heterogeneity ofindividual features (e.g., consistency/heterogeneity of number, area,fragment, intensity, roundness, etc.) among centrosomes within anindividual specimen, and consistency/heterogeneity of individualfeatures among centrosomes between different specimens.

For example, centrosomal texture features can be used. To calculatethese 13 texture features, first one needs to create a gray-levelco-occurrence matrix (GLCM) from a segmented centrosome image. Thencalculate 13 texture features from GLCM as follows (Haralick et al.(1973); Haralick and Shapiro (1992)):

Angular second moment

Contrast

Correlation

Sum of squares: Variance

Inverse difference moment

Sum average

Sum variance

Sum entropy

Entropy

Difference variance

Difference entropy

Information measures of correlation

Maximal correlation coefficient

(Definitions and formulas can be found from the references).

Elimination of Redundant Features.

In general, one does not need to keep the features which are redundant,i.e., strongly related to other features. If we adopt the correlationbetween the two variables as the measure of redundancy, we conclude thata feature is useful if it is not highly correlated to any of the otherfeatures (Michalak et al. (2006)).

Shape Features Selection.

Six features used to measure centrosomal shape are discussed herein.Correlations between every pair of these six features or other shapefeatures for both normal and untreated cancer cell centrosomes arecalculated (Michalak et al. (2006)). In an embodiment, a correlationbetween two features larger than 0.8 or less than −0.8 is considered tobe highly correlated. If no pair of features is highly correlated, nofeature is considered redundant, and all of the shape features are usedfor the centrosome's shape measurement.

Statistical Analysis

Two Sample T-Test.

After centrosome features are selected, the two sample t-test can beperformed to verify whether the two samples can be distinguished bythese features. The test is carried out under the assumption that thetwo samples are independent and normally distributed with equal meansunder the null hypothesis and different means under the alternativehypothesis.

The test result h=1 indicates rejection of the null hypothesis at a=5%significance (95% confidence) level; h=0 indicates failure to reject thenull hypothesis. The test returns the p-value p of the test and theconfidence interval ci, for the difference of means of the two samples.Although for small sample sizes, centrosome features are not necessarilynormally distributed, the central limit theorem guarantees that thesample mean is normally distributed, as long as the sample size is bigenough (N=30). The sample size N=57 and 606 in our study satisfies therequirement. Therefore the two sample t-test is applicable to our data(Terriberry et al. (2005)).

Two Sample Kolmogorov-Smirnov Test (KS-Test).

The Kolmogorov-Smirnov test is usually used to determine whether the twosamples are drawn from the same distribution (the null hypothesis) ordifferent distributions (the alternative hypothesis). The two-sample KStest is one of the most useful and general nonparametric methods forcomparing two samples, as it is sensitive to differences in bothlocation and shape of the empirical cumulative distribution functions ofthe two samples. The KS-test also has an advantage of making noassumption about the normal distribution of data. The test result h=1means rejection of the null hypothesis that distributions of the twosamples are the same at a=5% significance (95% confidence) level; thevalue h=0 indicates failure to reject this hypothesis. The test alsoreturns the p-value p, and the value of the test statistic k whichquantifies the difference between distributions of the two samples andcan be written ask=Max(|F ₁(x)−F ₂(x)|)

where F₁(x) and F₂(x) are empirical cumulative distribution functions ofsamples 1 and 2, respectively (Kozmann et al. (1991).

Results.

After image acquisition, in total, 606 centrosomes were selected fromuntreated cancer cells and 57 centrosomes were selected from normalcells. The correlations among centrosomal shape features were calculatedto determine feature redundancy. The Number/Cell and Fragment featuresare different in nature, and different from other features, therefore wepreserved Number/Cell and Fragment as independent features. Due to this,we did not calculate correlations between these two features or betweenthese two features and other nine features.

Correlations between the other nine shape features for both the normalcells and untreated cancer cells results are presented in Tables 1 and2.

Tables 1 and 2 show that centrosome features “Area” and “Mean Diameter”are highly correlated for both normal and untreated cancer cells(correlation coefficient 0.985 and 0.938, respectively), and therefore,one of these features is redundant. “Area” is the only feature whichdescribes centrosome size while “Mean Diameter” is one of six featureswhich describe centrosome shape. Hence, we have removed “Mean Diameter”from further investigation. After “Mean Diameter” is removed, theremaining 10 features are entered into the statistical analysis.

TABLE 1 Correlations between shape features of normal cell centrosomesMean Perim Fract Inten Area Asp Area/Box Dia Rdn Inten. ratio Dim StDevArea 1.000 −0.005 −0.319 0.985 0.496 0.067 −0.304 0.370 0.283 Asp −0.0051.000 −0.497 0.074 0.514 −0.261 −0.294 0.246 −0.257 Area/Box −0.319−0.497 1.000 −0.384 −0.716 0.147 0.621 −0.455 0.118 Mean Dia 0.985 0.074−0.384 1.000 0.533 0.041 −0.342 0.367 0.260 Rdn 0.496 0.514 −0.716 0.5331.000 −0.126 −0.695 0.750 −0.068 Inten. 0.067 −0.261 0.147 0.041 −0.1261.000 0.253 −0.147 0.732 Perim radio −0.304 −0.294 0.621 −0.342 −0.6950.253 1.000 −0.546 0.242 Fract Dim 0.370 0.246 −0.455 0.367 0.750 −0.147−0.546 1.000 −0.227 Inten StDev 0.283 −0.257 0.118 0.260 −0.068 0.7320.242 −0.227 1.000 Asp = Aspect, Dia = Diameter, Rdn = Roundness, Inten= Intensity, Perim = Perimeter, Fract = Fractal, Dim = dimension, StDev= Standard Deviation

TABLE 2 Correlation between features of untreated cancer cellcentrosomes Mean Perim Fract Inten Area Asp Area/Box Dia Rdn Inten.ratio Dim StDev Area 1.000 0.141 −0.361 0.938 0.713 0.293 −0.387 0.4060.412 Asp 0.141 1.000 −0.601 0.241 0.467 −0.192 −0.176 0.176 −0.234Area/Box −0.361 −0.601 1.000 −0.435 −0.714 0.229 0.564 −0.569 0.235 MeanDia 0.938 0.241 −0.435 1.000 0.698 0.347 −0.423 0.377 0.477 Rdn 0.7130.467 −0.714 0.698 1.000 −0.099 −0.673 0.729 −0.051 Inten. 0.293 −0.1920.229 0.347 −0.099 1.000 0.132 −0.220 0.699 Perim radio −0.387 −0.1760.564 −0.423 −0.673 0.132 1.000 −0.744 0.138 Fract Dim 0.406 0.176−0.569 0.377 0.729 −0.220 −0.744 1.000 −0.210 Inten StDev 0.412 −0.2340.235 0.477 −0.051 0.699 0.138 −0.210 1.000 Asp = Aspect, Dia =Diameter, Rdn = Roundness, Inten = Intensity, Perim = Perimeter, Fract =Fractal, Dim = dimension, StDev = Standard Deviation

The two sample t-test comparison between normal and untreated cancercentrosomes returned p-values less than 0.001 for all 10 features.Correspondingly, the 99.9% confidence intervals (ci) on the meandifferences of all 10 features do not contain zero. This statisticalresult rejects the null hypothesis, i.e., H=1 for all 10 features (seeTable 3). Based on the statistical test result, we can say with 99.9%confidence that for all 10 features there are significant meandifferences between normal and untreated cancer centrosomes.

The difference in the distributions of centrosomal features for normaland untreated cancer cells can be also seen from the box plots below. Wepresent box-plots for five centrosomal features: centrosomal number,size, fragment, intensity, and shape. From FIGS. 4A-4E, we can see thatthese five features have different medians and, overall, differentdistributions. The other five box plots show a similar pattern.

The two sample Kolmogorov-Smirnov test confirmed the boxplot results andare consistent with the two-sample t-test (see Table 4). The testverifies that all 10 centrosome features have different distributionsfor the normal and untreated cancer cells (h=1). The largest p-value is0.00015 which means that with 99.985% confidence we can claim thatdistribution of every feature is different for two types of cells. Thetest also returns the values of statistic k that indicates whether thedistances between cumulative distribution functions (CDFs) aresufficiently large to be distinct. The smallest value of k is 29.5%which indicates that the distances between CDFs of the centrosomefeatures for normal and untreated cancer cells are large enough todistinguish them.

We illustrate the CDF plots of 5 centrosomal features (see FIGS. 5A-5E):centrosomal number, size, fragment, intensity, and shape. One can seesubstantial differences between the shapes and positions of the CDFcurves for centrosomal features of normal and untreated cancer cells. Itis also apparent that the maximum distances (k) between pairs of curveare quite large. This means that all pairs of samples have differentdistributions and came from different populations. The remaining fiveCDF curves show a similar pattern.

Thus, the present invention can be used to distinguish untreated cancercells from normal cells through quantitative analyses of centrosomalfeatures. In an embodiment, cancer can thus be diagnosed according tothis method.

TABLE 3 Two Sample t-test result for Normal and Untreated cancer cellsPerim Fract Inten Num/Cell Frag. Area Asp Area/Box Rdn (ratio) DimInten. StDev h 1 1 1 1 1 1 1 1 1 1 p 0.000 0.000 0.622 0.001 0.000 0.2060.396 0.000 0.000 0.001 e−003 e−003 e−003 e−003 e−003 e−003 e−003 e−003e−003 e−003 ci −3.986 −0.719 86.693 −0.681 0.054 −0.786 0.011 −0.04626.536 −3.888 −2.337 −0.461 317.54 −0.294 0.117 −0.244 0.039 −0.02141.295 −1.700 Num = Number, Frag = Fragment, Asp = Aspect, Rdn =Roundness, Inten = Intensity, Perim = Perimeter, Fract = Fractal, Dim =dimension, StDev = Standard Deviation

TABLE 4 Two Sample Kolmogorov-Smirnov test for Normal and UntreatedCancer cells Perim Fract Inten Num/Cell Frag. Area Asp Area/Box Rdn(ratio) Dim Inten. StDev h 1 1 1 1 1 1 1 1 1 1 p 4.976 2.547 3.626 8.1072.789 1.052 1.597 2.213 1.046 1.662 e−024 e−013 e−016 e−008 e−008 e−006e−004 e−008 e−012 e−005 k 0.803 0.590 0.579 0.397 0.409 0.366 0.2950.412 0.511 0.329 Num = Number, Frag = Fragment, Asp = Aspect, Rdn =Roundness, Inten = Intensity, Perim = Perimeter, Fract = Fractal, Dim =dimension, StDev = Standard Deviation

Discussion

Described herein is an objective procedure for characterizing andquantifying centrosomal defects found in lung cancer cells, but that arenot found in normal cells. The term ‘centrosome amplification’ iscommonly used to signify centrosomes that subjectively appearsignificantly larger than normal (as defined by the specific staining ofstructural centrosome components in excess of that seen in thecorresponding normal tissue or cell type); supernumerary centrioles(more than four) in centrosomes; inverted polarity of centrosomelocation; and/or more than two centrosomes are present within a cell.Amplified centrosomes also show protein hyperphosphorylation and alteredfunctional properties such as an increased microtubule nucleatingcapacity (D'Assoro et al. (2008); Salisbury et al. (2004); Hontz et al.(2007)). These structural centrosome abnormalities have been implicatedas potential cause of loss of cell and tissue architecture seen incancer (i.e., anaplasia) through altered centrosome function, andresulting in chromosome missegregation during mitosis as a consequenceof multipolar spindle formation (Piel et al. (2001)).

Until now, researchers commonly detect the centrosome defects throughmicroscopy. Guo et al. have done limited image analysis of centrosomalfeatures, which include numerical and structural centrosomeamplification. The cell was considered to have structural centrosomeamplification if the diameter of its centrosome was greater than twicethe diameter of the normal centrosome and/or if the shape of itscentrosome became irregular (Guo et al. (2007)). These investigatorsapplied semi-quantitative image analysis of cells. Other approaches forquantitation of centrosome abnormalities have used semi-quantitativemicroscopy based procedures that cannot practically avoid subjectivejudgment even with highly-experienced microscopists.

The novel quantitative analysis and statistical inference of centrosomalfeatures, extracted from cell images using the subject invention avoidsthose pitfalls and provides objective assessment of centrosome features.The methods include quantitative measurement of a centrosome featuresprofile, capable not only of detecting feature differences, but also ofshowing the magnitude and consistency of these differences. The diameteris not sufficient to characterize the structure or shape of acentrosome. In one embodiment, five features have been used in theresearch herein to describe the centrosome shape representingnon-correlated aspects of centrosome morphology. Correspondingstatistical analysis of centrosome features show the significantdifferences of quantitatively measured features between normal andcancer centrosomes. Therefore, the present invention can be used todistinguish untreated cancer cells from normal cells throughquantitative analysis of centrosomal features. Quantitative calculationand analysis of centrosomal features can also serve as a marker formonitoring and/or predicting cancer progression as discussed herein.

Example 2 Discriminant and Prognosis of Stage I Long-Term and Short-TermSurvival Lung Cancer Patients Through Quantitative Analysis ofCentrosomal Features

Tissue Processing and Immunohistochemisty

35 cases of lung tissue with different forms and stage of cancer wereprovided from H. Lee Moffitt Cancer Center & Research Institute. Sampleswere processed within the Moffitt Microarray Core. Tissues were fixed informaldehyde, and then embedded in paraffin. For immunohistochemistry,sections were deparafinized using xylene and ethanol washes followed byantigen retrieval buffer (Dako). According to protocol, sections werewashed in PBS then blocked (10% normal goat serum, 3% BSA and 0.5%gelatin in PBS) for 1 hour at 4 C. Sections were incubated overnight at4 C in primary antibody anti-gamma Tubulin, produced in rabbit (Sigma,1:300 diluted in PBS with 2% Normal Goat Serum. Sections were washed inPBS-T, incubated with secondary antibody AlexaFlour 633 goat anti-rabbitIgG (Invitrogen, 1/200) for 1 hour, then rinsed in PBS-T. Sections werecounter-stained and mounted with Prolong Antifade solution w/DAPI(Invitrogen).

Image Acquisition

Centrosomal images were acquired in the Analytic Microscopy Core at theH. Lee Moffitt Cancer Center. A DMI6000 inverted Leica TCS AOBS SP5tandem-scanning confocal microscope was used to image the tissue, undera 100× oil immersion objective with scanning speed of 100-Hz per each2048×2048 frame. The LAS AF software suite was used to image the tissueand compile the max projections from Z-stacks. The acquired image has aresolution of 75.7 nm (see FIG. 6A).

Among the 35 cases which are totally scanned were six stage 1 NSCLCsurvivors (followed for nine years or more) and nine fatalities whosurvived four years or less. Of these stage 1 cases, six of thenine-year or more survivors and six cases who died after four-years orless are used for discriminant analysis. Among the 12 cases, nine-yearor more survival cases consist of four cases of stage 1A and two casesof stage 1B lung cancer; four-year or less survival cases consist ofthree cases of stage 1A and three cases of stage 1B lung cancer.

A Region of Interest (ROI) is selected to consist of one cell with atleast one centrosome (see FIGS. 1B and 1C). In total, 211 ROIs with 309centrosomes from four-year or less survival cases and 235 ROIs with 594centrosomes from nine-year or more survival cases have been acquired forthis experiment.

Image Processing

Image Enhancement

Since the centrosome is a very small cellular organelle, 75.7 nmresolution is generally not satisfactory to distinguish centrosomefeatures, such as shape, boundary and structure analysis. Enhancementhas been performed to further increase ROI images' resolution. Twodimensional first degree Lagrange polynomial interpolation (Berrut andTrefethen (2004)) is implemented to enhance resolution of the images.This is a linear interpolation technique which, at any point, usesinformation given only by the two adjacent pixels and leads to a goodimage approximation.

Image Segmentation

After enhancement and before extracting centrosomal features, thecentrosomes need to be isolated from other parts (background) of thecell images. After comparing various thresholding methods, Kapur'smaximum entropy-based thresholding (Yin (2002)) was selected andimplemented for this task due to the consistency and accuracy of itsoutputs. The method considers the foreground (centrosomes) and thebackground (other parts of the cells) of an image as two differentsignal sources and finds the threshold which maximizes the sum of theentropies of the two classes as follows.

Let an image have N pixels with gray level ranging from 0 to L−1. Denoteby h(i), the number of occurrences of gray level i, and by P_(i)=h(i)/N,the probability of occurrences of gray level i. The method findsthreshold t which maximizes

f(t) = H(0, t) + H(t, L) where${{H\left( {0,t} \right)} = {- {\sum\limits_{i = 0}^{t - 1}\;{\frac{P_{i}}{w_{0}}\ln\;\frac{P_{i}}{w_{0}}}}}},{w_{0} = {\sum\limits_{i = 0}^{t - 1}\; P_{i}}},{{H\left( {t,L} \right)} = {- {\sum\limits_{i = t}^{L - 1}\;{\frac{P_{i}}{w_{1}}\ln\;\frac{P_{i}}{w_{1}}}}}},{w_{1} = {\sum\limits_{i = t}^{L - 1}\;{P_{i}.}}}$The entropy threshold got consistently accurate segmentation (see FIGS.1D and 1E).Feature Extraction and OptimizationFeature Extraction

After centrosomes are isolated, 12 specific centrosomal features areextracted, to be later used for discrimination between long term andshort term survival cases. The definitions of these 12 features are asfollowing:

-   -   (1) Number—Number of centrosomes per cell.    -   (2) Area—The number of pixels in the area of a centrosome.    -   (3) Area/Box—The ratio between the numbers of pixels in the area        of a centrosome and the area of its bounding box. It is always        less than or equal to 1.    -   (4) Aspect—The ratio between the major axis and the minor axis        of the ellipse which is equivalent to a centrosome (has the same        area as the centrosome). Aspect is always greater than or equal        to 1.    -   (5) Hole Ratio—Ratio of centrosomal area excluding holes to        total area of centrosome.    -   (6) Perimeter ratio—The ratio between the convex perimeter of a        centrosome and its actual perimeter. Perimeter ratio is always        less than or equal to 1.    -   (7) Roundness—Roundness is equal to the squared perimeter of a        centrosome divided by 4πA, where A is the area of the        centrosome. Roundness demonstrates how far the shape of the        centrosome deviates from a circle. The larger the roundness        parameter, the further the deviation of the shape from being        round. If a centrosome has a circular shape, its roundness is        equal to one, otherwise, it is greater than one.    -   (8) Fractal dimension (Addison (1997))—The fractal dimension is        a measurement of roughness. The rougher the curve, the larger        the fractal dimension. The general expression of fractal        dimension is

${FD} = {\lim\limits_{S\rightarrow 0}\frac{\mathbb{d}\left( {\log(N)} \right)}{\mathbb{d}\left( {\log\left( {1\text{/}S} \right)} \right)}}$where N is the number of hypercubes (for example, square) of side lengthS required to cover the object (for example, a curve).In practice, the box counting dimension can be estimated by selectingtwo sets of [log(N), log(1/S)] coordinates at small value of S. Anestimate of Fragment Dimension FD is then given by,

${FD} = {\frac{{\log\left( N_{2} \right)} - {\log\left( N_{1} \right)}}{{\log\left( {1\text{/}S_{2}} \right)} - {\log\left( {1\text{/}S_{1}} \right)}} = \frac{\log\frac{N_{2}}{N_{1}}}{\log\frac{S_{1}}{S_{2}}}}$

-   -   (9) Intensity—An average gray level intensity in a centrosomal        area is obtained by adding pixel values over the centrosomal        area and then dividing by the area of the centrosome.    -   (10) Intensity standard deviation—The standard deviation of the        gray level intensity in the centrosomal area.    -   (11) Solidity—The proportion of the pixels in the convex hull        that are also in the region. Computed as Area/ConvexArea.    -   (12) Eccentricity—The eccentricity is the ratio of the distance        between the foci of the ellipse and its major axis length. The        value is between 0 and 1. (0 and 1 are degenerate cases; an        ellipse whose eccentricity is 0 is actually a circle, while an        ellipse whose eccentricity is 1 is a line segment.)        These 12 features can be classified into six categories:    -   I. Centrosome Number: Number/Cell,    -   II. Centrosome Size: Area.    -   III. Centrosome Shape: Aspect, Area/Box, Roundness, Perimeter        Ratio, Solidity, and Eccentricity.    -   IV. Centrosome Boundary: Fractal Dimension.    -   V. Centrosome Structure: Hole Ratio.    -   VI. Centrosome Intensity: Mean Intensity and Intensity Standard        Deviation.        Feature Selection and Optimization

Feature selection or feature set optimization is a critical issue indiscriminant analysis or classification. The purpose of featureselection is: 1) Feature set reduction to reduce the computation and 2)Reduction of noise to improve the classification accuracy. Featureselection algorithms can be roughly grouped into two categories: filtermethods and wrapper methods. Filter methods rely on generalcharacteristics of the data without involving the chosen learningalgorithm. Wrapper methods use the performance of the chosen learningalgorithm to evaluate each candidate feature subset. Peng et al.developed a feature selection algorithm called “minimumredundancy—maximum relevance (MRMR) feature selection” (Peng et al.(2005); Ding and Peng (2005)). MRMR is a filter method. This methodselects features by testing whether some preset conditions about thefeatures and the target class are satisfied. It often yields comparableclassification errors and high generalization of the selected featuresfor different classifiers with low cost of computation. MRMR provides amore balanced coverage of the space and capture broader characteristicsof phenotypes.

Mutual information is a measure of relevance of classes. Biggerdifference for difference classes should have larger mutual information.Given two random variables x and y, their mutual information is definedbased on their joint probabilistic distribution p(x, y) and densityfunctions p(x), p(y).

$\begin{matrix}{{I\left( {x,y} \right)} = {\sum\limits_{i,j}\;{{p\left( {x_{i},y_{j}} \right)}\log\frac{p\left( {x_{i},y_{j}} \right)}{{p\left( x_{i} \right)}{p\left( y_{j} \right)}}}}} & {{for}\mspace{14mu}{discrete}\mspace{14mu}{variables}} \\{{I\left( {x,y} \right)} = {\int{\int{{p\left( {x_{i},y_{j}} \right)}\log\frac{p\left( {x_{i},y_{j}} \right)}{{p\left( x_{i} \right)}{p\left( y_{j} \right)}}{\mathbb{d}x}{\mathbb{d}y}}}}} & {{for}\mspace{14mu}{continous}\mspace{14mu}{variables}}\end{matrix}$The minimum redundancy condition is:

$\begin{matrix}{{\min\; W_{I}},{W_{I} = {\frac{1}{{S}^{2}}{\sum\limits_{i,{j\;\varepsilon\; S}}\;{I\left( {x_{i},x_{j}} \right)}}}}} & (5)\end{matrix}$where |S| is the number of features in S.The maximum relevance condition is:

$\begin{matrix}{{\max\; V_{I}},{V_{I} = {\frac{1}{{S}^{2}}{\sum\limits_{i\;\varepsilon\; S}\;{I\left( {x_{i},c} \right)}}}}} & (6)\end{matrix}$where c is the target class.

The MRMR feature set is obtained by optimizing the two conditionssimultaneously. The order of our original 12 features are:

1 2 3 4 5 6 7 8 9 10 11 12 Num/ Area Aspect Area/ Hole Round- Inten.Perim. Fractal Inten. Solidity Eccen- cell Box Ratio. ness Ratio Dimen.Stdev. tricity

The optimized order by MRMR is:

9 6 2 1 8 7 3 5 4 12 10 11

Then we test the performance of a classifier, linear discriminantanalysis (LDA) with the feature number from one to 12 selected accordingto the optimized order. 10-fold cross-validation has been performedthree times for every number of features. The results are shown in Table5. We chose average of the three times test as test result. Thedistribution of error rate can be seen in FIG. 7. The error rate reachedminimum when six features were selected (member/cell, area, roundness,intensity, perimeter ratio, fractal dimension). We used these sixfeatures as our feature set for statistical analysis, discriminantanalysis, and classification.

TABLE 5 Error rate of 10-fold cross validation on linear discriminantanalysis Feature # 1 2 3 4 5 6 7 8 9 10 11 12 First test 0.3677 0.38430.3167 0.3145 0.2746 0.2614 0.2636 0.2658 0.2713 0.2669 0.2636 0.268 2nd test 0.3677 0.3798 0.3134 0.3123 0.2724 0.2602 0.2702 0.2647 0.27240.2691 0.2658 0.2702 3rd test 0.3677 0.3754 0.3156 0.3134 0.2735 0.26360.2647 0.268  0.2658 0.268  0.2702 0.2724 Average 0.3677 0.3798 0.31520.3134 0.2735 0.2617 0.2662 0.2662 0.2698 0.2680 0.2665 0.2702Statistical Analysis

1) Two-Sample T-Test

Two-sample tests can be used in either a descriptive or experimentaldesign. In a descriptive design, two samples are randomly drawn from twodifferent populations. If the analysis yields a significant difference,we conclude that the populations from which the samples were drawn aredifferent. The test is carried out under the assumption that the twosamples are independent and normally distributed with equal means underthe null hypothesis (h=0) and different means under the alternativehypothesis (h=1). For small sample sizes, centrosome features may not benormally distributed; the central limit theorem guarantees that thesample mean is normally distributed, as long as the sample size is bigenough (N≧30). Our sample sizes are N=309 and 594, respectively, whichsatisfies the requirement. Therefore, the two-sample t-test isapplicable to our data (Terriberry (2005)).

2) Wilcoxon Rank Sum Test or Two-Sided Rank Sum Test

Wilcoxon rank-sum test is a non-parametric alternative to the two-samplet-test. Non-parametric statistics are not limited by parametricrestrictions; it is sometimes called distribution-free method because itis not necessary to assume that the samples are normally distributed.Wilcoxon rank-sum test is much less sensitive to outliers than thetwo-sample t-test. These advantages make it more suitable for testingsmall samples with un-normal distribution and outliers. The nullhypothesis of Wilcoxon rank sum test is that the two samples areindependent from identical continuous distributions with equal medians,against the alternative that they do not have equal medians.

3) Kolmogorov-Smirnov (KS) Test

The Kolmogorov-Smirnov test is usually used to determine whether the twosamples are drawn from the same distribution (the null hypothesis) ordifferent distributions (the alternative hypothesis). The two-sample KStest is one of the most useful and general nonparametric methods forcomparing two samples, as it is sensitive to differences in bothlocation and shape of the empirical cumulative distribution functions ofthe two samples. The KS-test also has an advantage of making noassumption about the normal distribution of data.

Except h and p, the K-S test also returns the test statistic k, whichquantifies the difference between distributions of the two samples andcan be written as:k=Max(|F ₁(x)−F ₂(x)|)where F₁(x) and F₂(x) are empirical cumulative distribution functions ofsamples 1 and 2, respectively (Kozmann et al. (1991)).Classification

1) Linear Discriminant Analysis

Linear discriminant analysis (LDA) is a well-known classificationtechnique (Qiao et al (2009)). The approach of LDA is to project all thedata points into new space of lower dimension, which maximizes thebetween-class variability and minimizes their within-class variability.For two categories of classification, the LDA finds an axis and projectsall data points on this axis for distinguishing between the two classes.Allocation of a new point to a class can be accomplished by using adistance measurement. LDA is essentially a projection method.

2) Support Vector Machine

In general, Artificial Neural Network (ANN) or Support Vector Machine(SVM) outperforms LDA (Kumar and Bhattacharya (2006); Gokcen and Peng(2002)). A Support Vector Machine performs classification bytransforming a nonlinear input data into higher dimensional space byusing an appropriate kernel; then in the transformed space the data willbe linearly separable. In SVM literature, a predictor variable is calledan attribute, and a transformed attribute that is used to define thehyperplane is called a feature. A set of features that describes onecase is called a vector. So, the goal of SVM modeling is to find theoptimal hyperplane that separates clusters of vectors, cases with onecategory being on one side of the plane and cases with the othercategory being on the other side.

Results

1) Two-Sample T-Test Result

TABLE 6 Two-sample t-test of 9 year survival vs. fatality after 4 yearssurvival α = 0.05 Num/cell Area Roundness Intensity PerimRatioFractalDimen h 1 1 1 1 1 1 p 3.04E−07 1.02E−13 5.32E−22 0.0007472.22E−33 1.6858E−36 ci −1.465 168.788 0.554 −10.631 −0.107 0.070 −0.661287.244 0.827 −2.826 −0.078 0.094

The test result for all six features h=1 indicates rejection of the nullhypothesis, which means the two samples for all six features havedifferent means and come from different populations. Returned p-valuesless than 0.001 for all six features indicate that the 99.9% confidenceintervals (ci) on the mean differences of all six features do notcontain zero, with 99.9% confidence that for all six features, there aresignificant mean differences between two populations. This result alsosuggests a feasibility to distinguish these two populations, which canbe seen from FIGS. 8A-8F.

2) Wilcoxon Rank Sum Test or Two-Sided Rank Sum Test Result

TABLE 7 Wilcoxon rank sum test of 9 years vs. 4 years survival α = 0.05Fractal- Num/cell Area Roundness Intensity PerimRatio Dimen h 1 1 1 1 11 p 7.01E−06 6.71E−27 6.45E−37 9.70E−04 1.57E−35 2.76E−37The result rejects the null hypothesis for all six features withp-values less than 0.001, which indicates there are significant mediandifferences between two different populations, with 99.9% confidence forall six features. The result is shown in the box plots in FIGS. 10A-10F.

3) Kolmogorov-Smirnov (KS) Test Result

TABLE 8 Two-sample K-S test of 9 year vs. 4 year survival α = 0.05Fractal- Num/cell Area Roundness Intensity PerimRatio Dimen h 1 1 1 1 11 p 0.0015 5.87E−31 8.48E−34 4.20E−03 1.85E−30 1.87E−39 k 0.178 0.41220.4309 0.1221 0.4088 0.466The two-sample Kolmogorov-Smirnov test is consistent with the two-samplet-test and Wilcoxon rank-sum test (see Tables 6, 7, and 8). The testverifies that all 6 centrosome features have different locations andshapes for four-year and nine-year survival patients (h=1). The largestp-value is 0.0015, which means that with 99.85% confidence, we can claimthat distribution of every feature is different for two types ofsurvival terms. The test also returns the values of statistic k thatindicate whether the distances between cumulative distribution functions(CDFs) are sufficiently large enough to be considered distinct. Fourfeatures' k are bigger than 40% and the smallest value of k is 12.2%,which indicates that the distances between CDFs of the centrosomefeatures for four-year and nine-year survival patients are large enoughto distinguish them. The comparison is shown in FIGS. 9A-9F.

Three different statistical analysis methods have been carried out.These three methods quantitatively analyzed the data of the two samplesfrom different aspects such as mean, median, location and shape. All thethree methods have consistently proven that these two samples are fromdifferent populations. Therefore, they are distinguishable or can beclassified. To verify how well they can be classified, we have appliedtwo different classifiers on this data.

Classification

1) Result of Linear Discriminant Analysis

Training and Testing

The total of 903 centrosomes are split into training group and testinggroup. Even order numbers are selected for training and odd ordernumbers are selected for testing. The result is shown in Table 9.

TABLE 9 Training and testing result of LDA Categories Number Error rateAccurate rate Sensitivity Specificity Training 451 0.2683 0.7317 0.79870.6970 Testing 452 0.2655 0.7345 0.8323 0.6835 Total 903 0.2669 0.73310.8155 0.6902Since the training data and testing data are selected (either manuallyor randomly), the training data may not represent the whole data.Results may vary if the classification is repeated with a differentselection of training data and testing data. To avoid this variation andachieve overall performance evaluation, K-fold cross-validation has beenperformed (Kohavi (1995)). In K-fold cross-validation, the originalsample is randomly partitioned into K subsamples. Of the K subsamples, asingle subsample is retained as the validation data for testing theclassifier, and the remaining K−1 subsamples are used as training data.The cross-validation process is then repeated K times (the folds), witheach of the K subsamples used exactly once as the validation data. The Kresults from the folds then can be averaged to produce a singleestimation. In this experiment, 10-fold cross-validation has beenperformed. The result is shown in Table 10:

TABLE 10 10-fold cross-validation result of LDA Error rate Accurate rateSensitivity Specificity First test 0.2614 0.7386 0.8026 0.7054 Secondtest 0.2602 0.7398 0.8155 0.7003 Third test 0.2636 0.7364 0.8058 0.7003Average 0.2617 0.7383 0.8080 0.7020The advantage of this method is that all observations are used for bothtraining and validation, and each observation is used for validationexactly once. Therefore, the performance estimation represents anoverall performance of a classifier on the whole data. Since the groupsare selected randomly, there is small fluctuation for a different test.We tested three times and took the average as the result.Compare table 9 and table 10, we can see these results are very close,which means the method we used for selection of training data andtesting data is stable and reliable.

2) Classification Result of Support Vector Machine

For comparison, 10-fold cross-validation has been performed on SVM. Theresult is shown in Table 11. Compare Table 11 and Table 10; the accuraterate of SVM is somewhat better than LDA. The sensitivity of SVM isbetter than LDA. The specificity of LDA is better than SVM, which meansLDA is more balanced on both categories than SVM for classification ofthis data.

TABLE 11 10-fold cross-validation result of SVM (Linear kernel) Errorrate Accurate rate Sensitivity Specificity First test 0.2140 0.78600.8395 0.6832 Second test 0.2143 0.7857 0.8394 0.6825 Third test 0.21380.7862 0.83395 0.6836 Average 0.2140 0.7860 0.8376 0.6831

CONCLUSION

The results show that individual long-term survival and fatality aftershort-term survival of stage I lung cancer patients can be distinguishedby analysis and classification of centrosome features. Therefore,methods of the subject invention can be used to help doctors to designtherapy for the individual patient.

DISCUSSION

Since the classification object will not be individual centrosome,instead it will be individual patient case, which includes a group ofcentrosomes; thus, it is beneficial to classify a whole group ofcentrosomes into either a long-term survival category or a short-termsurvival category. Majority criterion will be applied in this caseclassification (Chiclana et al. (1995)). If a majority of centrosomes ina case is classified into the long-term survival category, the case willbe classified into long-term survival category and vice versa. Thiscriterion may increase sensitivity, specificity, and accuracy rate,since a patient case will be classified into the correct category if andonly if more than 50% of the centrosomes of the patient analyzed will beclassified into a correct category. After working with a well-selectedclassifier, any case will be able to be classified into one of the twocategories in a high accuracy rate.

All patents, patent applications, provisional applications, andpublications referred to or cited herein are incorporated by referencein their entirety, including all figures and tables, to the extent theyare not inconsistent with the explicit teachings of this specification.

It should be understood that the examples and embodiments describedherein are for illustrative purposes only and that various modificationsor changes in light thereof will be suggested to persons skilled in theart and are to be included within the spirit and purview of thisapplication and the scope of the appended claims. In addition, anyelements or limitations of any invention or embodiment thereof disclosedherein can be combined with any and/or all other elements or limitations(individually or in any combination) or any other invention orembodiment thereof disclosed herein, and all such combinations arecontemplated with the scope of the invention without limitation thereto.

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We claim:
 1. One or more computer-readable media having computer-useableinstructions embodied thereon for performing a method for diagnosingcancer and/or providing a prognosis for a person or animal, the methodcomprising: receiving an image of one or more cells; selecting a regionof interest that comprises one cell, wherein the cell comprises at leastone centrosome; segmenting the selected region of interest for the cell,wherein each at least one centrosome of the cell is delineated fromother parts of the cell; extracting at least one feature from each ofthe at least one delineated centrosome of the cell; analyzing the atleast one extracted feature from each of the at least one delineatedcentrosome of the cell; and diagnosing cancer and/or providing aprognosis based on one or more results of the analysis.
 2. The media ofclaim 1, wherein one or more of the at least one extracted feature iscentrosome number per cell, centrosome area, fragment, intensity,intensity standard deviation, area to box ratio, aspect, mean diameter,perimeter ratio, roundness, fractal dimension, solidity, oreccentricity.
 3. The media of claim 1, wherein the analysis comprises astatistical analysis.
 4. The media of claim 1, wherein the image isacquired via a tandem-scanning confocal microscope.
 5. The media ofclaim 1, wherein at least six centrosomal features are extracted andanalyzed.
 6. The media of claim 5, wherein the at least six centrosomalfeatures comprise number/cell, area, roundness, intensity, perimeterratio, and fractal dimension.
 7. The media of claim 1, wherein at leastfive centrosomal features are extracted and analyzed.
 8. The media ofclaim 7, wherein the at least five centrosomal features comprisenumber/cell, area, intensity, fragment, and aspect.
 9. The media ofclaim 1, wherein increased centrosomal number/cell; deviated area;deviated intensity; fragment; and/or deviated aspect is associated withdetection or a diagnosis of cancer.
 10. The media of claim 1, whereinone or more of the steps of the method are performed by one or moresuitably programmed computers and wherein computer executableinstructions for performing one or more of the steps of the method areprovided on the one or more computer readable media.
 11. A method fordetecting cancer, diagnosing cancer, and/or providing a prognosis for aperson or animal, the method comprising: obtaining an image of one ormore cells; selecting a region of interest that comprises one or morecells, wherein the cell comprises at least one centrosome; segmentingthe selected region of interest for the cell, wherein the at least onecentrosome of the cell is delineated from other parts of the cell;extracting at least one feature from each of the at least one delineatedcentrosome of the cell; analyzing the extracted feature from each of theat least one delineated centrosome of the cell; and detecting ordiagnosing cancer and/or providing a prognosis based on one or moreresults of the analysis.
 12. The method of claim 11, wherein one or moreof the at least one extracted feature is centrosome number per cell,centrosome area, fragment, intensity, intensity standard deviation, areato box ratio, aspect, mean diameter, perimeter ratio, roundness, fractaldimension, solidity, or eccentricity.
 13. The method of claim 11,wherein the image is acquired via a tandem-scanning confocal microscope.14. The method of claim 11, the method further comprising enhancing theimage of the one or more cells.
 15. The method of claim 11, wherein atleast six centrosomal features are extracted and analyzed.
 16. Themethod of claim 15, wherein the at least six centrosomal featurescomprise number/cell, area, roundness, intensity, perimeter ratio, andfractal dimension.
 17. The method of claim 11, wherein at least fivecentrosomal features are extracted and analyzed.
 18. The method of claim17, wherein the at least five centrosomal features comprise number/cell,area, intensity, fragment, and aspect.
 19. The method of claim 11,wherein increased centrosomal number/cell; deviated area; deviatedintensity; fragment; and/or deviated aspect is associated with detectionor a diagnosis of cancer.
 20. The method of claim 11, wherein one ormore of the steps of the method are performed by one or more suitablyprogrammed computers and wherein computer executable instructions forperforming one or more of the steps of the method are provided on one ormore computer readable media.
 21. The method of claim 11, wherein theresults of the analysis are stored on a computer-readable medium ordevice.
 22. The method of claim 11, wherein the method is performedusing an image processing system.
 23. A method for predicting a responseof a cancer or tumor to a therapeutic treatment, wherein said cancer ortumor exhibits defects associated with centrosomal amplification, saidmethod comprising contacting a cancer or tumor cell with a therapeuticagent for a sufficient period of time and then determining whether thetherapeutic agent reverses or ameliorates in the cancer or tumor cellone or more defects associated with centrosomal amplification using amethod comprising: receiving an image of one or more cells; selecting aregion of interest that comprises one cell, wherein the cell comprisesat least one centrosome; segmenting the selected region of interest forthe cell, wherein each at least one centrosome of the cell is delineatedfrom other parts of the cell; extracting at least one feature from eachof the at least one delineated centrosome of the cell; and analyzing theat least one extracted feature from each of the at least one delineatedcentrosome of the cell.
 24. The method of claim 23, wherein the defectsassociated with centrosomal amplification are mitotic spindle defectsand segregation defects.
 25. A method for monitoring a response of acancer or tumor to a therapeutic treatment, wherein said cancer or tumorexhibits defects associated with centrosomal amplification, said methodcomprising contacting a cancer or tumor cell with a therapeutic agentfor a sufficient period of time and then determining whether thetherapeutic agent reverses or ameliorates in the cancer or tumor cellone or more defects associated with centrosomal amplification using amethod comprising: receiving an image of one or more cells; selecting aregion of interest that comprises one cell, wherein the cell comprisesat least one centrosome; segmenting the selected region of interest forthe cell, wherein each at least one centrosome of the cell is delineatedfrom other parts of the cell; extracting at least one feature from eachof the at least one delineated centrosome of the cell; and analyzing theat least one extracted feature from each of the at least one delineatedcentrosome of the cell.